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Selective Ultrafilter P-Ideal Dichotomy Forcing Axioms Slim tree Diamond Erdos Cardinal Reduced Power Forcing Subtle cardinal Mandelbrot set Singular cofinality reflection principles L-space Luzin set Sierpinski's onto mapping principle Greatly Mahlo Singular cardinals combinatorics Well-behaved magma Partition Relations GMA Sakurai's Bell inequality Distributive tree polarized partition relation Universal Sequences super-Souslin tree Countryman line Almost Souslin Whitehead Problem Prevalent singular cardinals Partition relations for trees Knaster club_AD Square-Brackets Partition Relations Uniformly coherent Postprocessing function Open Access Foundations Uniformly homogeneous square principles Ineffable cardinal Hereditarily Lindelöf space Rainbow sets Martin's Axiom Strongly compact cardinal Cohen real Constructible Universe Subadditive Jonsson cardinal Cardinal Invariants Diamond-sharp regressive Souslin tree unbounded function Weakly compact cardinal Prikry-type forcing Knaster and friends Generalized Clubs free Souslin tree Chang's conjecture Rado's conjecture Successor of Singular Cardinal Non-saturation coloring number full tree Precaliber O-space Small forcing Iterated forcing perfectly normal Monotonically far Ramsey theory over partitions Ascending path incompactness free Boolean algebra Closed coloring Analytic sets ZFC construction Kurepa Hypothesis higher Baire space Amenable C-sequence Poset stationary hitting specializable Souslin tree Chromatic number square stick Fat stationary set Strong coloring Subtle tree property Filter reflection Aronszajn tree b-scale Nonspecial tree Minimal Walks tensor product graph Parameterized proxy principle Ulam matrix middle diamond Shelah's Strong Hypothesis Dowker space weak Kurepa tree Diamond for trees strongly bounded groups weak diamond S-Space AIM forcing Hedetniemi's conjecture Lipschitz reduction Coherent tree Was Ulam right? positive partition relation Fast club Strongly Luzin set Rock n' Roll diamond star Reflecting stationary set Almost countably chromatic Club Guessing ccc C-sequence approachability ideal transformations xbox Interval topology on trees Hindman's Theorem Commutative projection system Respecting tree Ostaszewski square nonmeager set Forcing with side conditions 54G20 PFA(S)[S] Almost-disjoint family Erdos-Hajnal graphs Entangled linear order Absoluteness very good scale Generalized descriptive set theory Vanishing levels SNR Antichain Microscopic Approach PFA Uniformization Fodor-type reflection Intersection model Souslin Tree OCA Subnormal ideal stationary reflection countably metacompact HOD weak square projective Boolean algebra Ascent Path sap Singular Density Dushnik-Miller Axiom R indecomposable filter Cardinal function Commutative cancellative semigroups Sigma-Prikry Large Cardinals Local Club Condensation. Successor of Regular Cardinal
Tag Archives: Singular Density
On topological spaces of singular density and minimal weight
Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading
Workshop on Set Theory and its Applications, February 2007
These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … Continue reading
On the consistency strength of the Milner-Sauer conjecture
Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading
